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From: mackw@bytex.com
Subject: Re: Fuzzy theory or probability theory? 
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In article <hubey.786314318@pegasus.montclair.edu>, 
<hubey@pegasus.montclair.edu> writes:
> sthomas@decan.gate.net (S. F. Thomas) writes:
> 
> >Like Watanabe (1978), I also find it difficult to accept the
> >result of the Zadehian min-max calculus that the fuzzy term "tall and
> >not tall" should be anything less than the logical absurdity, as the 
law of
> >contradiction requires.  One would lose all credibility as a witness
> >in court if one were to testify that the burglar was "tall, but not
> >tall".

When I was in college, one of the forwards on the basketball team was 
6'6" and was routinely described as not being tall.  Seeing him around 
campus, I had an entirely different opinion.  He was both tall and not 
tall or, more correctly, he was tall to a high degree, but was still not 
tall to some degree.  He was not completely tall or completely not tall, 
much less completely tall *and* completely not tall.

As to a witness in court, I would not be surprised to hear a description 
that "the burglar was tall but not too tall."  Again the interpretation 
of the statement from a fuzzy logic view is that tall is not an absolute 
characteristic, but one of degrees.  Likewise "not too tall" can be 
interpretted as "not tall to a low degree."

Fuzzy logic basically redefines the meaning of "truth" to allow degrees 
of truth.  Within the boundaries of its definitions, fuzzy logic appears 
(at least to me) to be self consistent,  and it also models, at least in 
 some cases, descriptions used in the real world, which would imply that 
fuzzy logic may also be useful.

Wayne Mack

